This is due to hard feelings from when the Navy abandoned the Marines at Guadalcanal. Also tradition and territory is so important in the military. They aren't really capable of making some monumental change like doing away with Marine aviation.
It's not so much that (Marine aviation existed before the U.S. entered World War I) and more to do with the fact that the Navy and Marines have entirely different aviation missions. The Navy specializes in fleet defense, naval warfare, and light bombing while the Marines specialize in close air support. Different mission specializations, unsurprisingly, call for entirely different technical requirements. Even if the Marines didn't have their own aviation, they would still need close air support from the Navy, and the requirement for a STOVL aircraft would still exist.
